Is there a way to add hair texture to 2d?
Yes, you can add a texture of hair exactly the same way you add any other textures for shaders for the rendering engine you use.

Will it look hyper-realistic or realistic or even good? Most likely no. Hair is visible outside the surface and because of that in most situations making hair in CG requires some sort of structure. There are many ways to create hair in Blender: hair particles could be used in multiple different ways or you could also use geometry with transparent textures, in some specific situations displacement or sculpting combined with texturing may work.